Moderation analysis

Three moderation analyses are supported:

Case 1: A single moderator variable
Case 2: Two independent moderator variables
Case 3: Two dependent moderator variables

Two types of graphs are available for moderation analyses. For case 1, one of each type will be produced, for the other two cases three graphs of each type will be produced. Definitions for elements of the graphs are given for Case 1 but applies equally to the other two cases.

Case 1: One moderator

In Case 1, the predictor or moderator variable X2 moderates the relationship between the focal variable X1 and the outcome. This corresponds to the equation

The program can accommodate a same level interaction term such as X1*X2 at any level of the model. Below are two examples of moderation analyses of this type of model. Either of the two predictors in a model can be selected as the focal variable, with the remaining variable serving as moderator variable. The choice is dependent on the researcher’s theoretical framework.

To request graphs, the focal and moderator variables are specified on the Settings page as shown below before accessing the Graphing page.

Simple slopes graph:

The first of the available graphs is a plot of the conditional regression line(s) describing the relationship between the outcome and the focal predictor as a function of the moderator. The plot will automatically show a line at each of three values of the moderator variable: mean – 1 standard deviation, mean, and mean + 1 standard deviation. In other words, the value of the moderator variable is held constant at three specific values. Values of the focal variable are used to define the x-axis, and the plot is confined to the area (mean of focal variable – 2 standard deviations, mean of focal variable + 2 standard deviations). Here is an example of a simple slopes graph using default graph parameter settings:

The graph is produced as a *.png file which can easily be inserted into a paper. A number of graph settings may also be modified by the user on the Graphing page within the program. To access the graphs, use the Run page.

Confidence interval graph: The second graph shows the regression line describing the relationship between the outcome and the focal predictor as a function of the moderator, along with a 95% confidence interval. It also shows the so-called region of significance, provided that the boundaries of this region fall within the scale set by the values of the moderator variable, which again defines the x-axis. The region between the lower and upper bound of the region of significance indicates the values of the moderator for which the slope of the regression of outcome on focal variable transitions from non-significance to significance. An example of the confidence interval graph with regions of significance is shown below.

Case 2: Two independent moderators

Consider the case where the relationship between the outcome and a predictor (denoted as X3 in the image below) is moderated by two predictors (X1 and X2). While it is assumed that these two variables moderate the relationship, they are independent of each other.

This corresponds to the equation

Again, focal and moderator variables may be at any level of the hierarchy. Here is an example of such a model, occurring at level-1 of the hierarchy. The relationship between the outcome MATHACH and the focal variable SES is moderated by the two independent variables MINORITY and FEMALE.

In this case, three simple slopes and three confidence interval graphs are produced, one for each of three values of the second moderator variable. Similarly, three confidence interval graphs are produced, as shown below. In all cases, values of the first moderator variables define the x-axis.

To access the graphs, use the Run page. Note that they can also be downloaded together with all files used in the analysis. To change graph parameters, use the Graphing page. The graphs will be displayed on the Run page, from where they may be copied as well.

Case 3: Two dependent moderators

In this case, there are again two predictors moderating the relationship between the outcome and a focal predictor (denoted as X3) in the image below. However, in contrast with Case 2, where two independent moderators are present, here the two moderators X1 and X2 are dependent.

This corresponds to the equation

Case 3 includes two-way interaction terms and a three-way interaction term between the focal variable (X3) and the two moderators (X1,X2). Below is an example of such a moderation analysis set up on the intercept equation at level-2. The variable DISCLIM serves as the focal variable, with SIZE and SECTOR the two dependent moderators.

There is again no restriction in terms of which level this may be specified at. Keep in mind that the program does not allow any higher-level interaction than a three-way interaction, so while it is possible to specify this model on, say, the intercept equation at a higher level, it will not be possible to do so on a slope equation.

Graphs produced for this case are like those produced in Case 2: 3 simple slope graphs, and three confidence intervals graphs are created. To change graph parameters, use the Graphing page. The graphs will be displayed on the Run page, from where they may be copied as well.